The Value of ABS[?]

Date: 08/24/2010 at 22:18:19
From: Jen
Subject: When you use absolute value in finding roots?
In class sometimes when the teacher is at the board doing problems with
roots and lots of variables, all of a sudden an absolute value symbol will
appear in the answer.
When exactly does this pair of vertical lines come into play?

Date: 08/25/2010 at 10:11:27
From: Doctor Ian
Subject: Re: When you use absolute value in finding roots?
Hi Jen,
Suppose I know that the value of some variable, if squared, is equal
to 4:
x^2 = 4
There are TWO solutions to this equation -- one positive, and one
negative:
x^2 = 4
x = 2 or -2
The absolute value symbol is a way of specifying both of those values
at once:
x^2 = 4
x = 2 or -2
|x| = 2 This means the same thing as
the previous line.
It's just a convenience, so you don't have to keep writing subsequent
equations twice (once for the positive value, and again for the negative
value).
Does it make more sense now?
- Doctor Ian, The Math Forum
http://mathforum.org/dr.math/